Pertanyaan

Hasil pemangkatan dari ( 4 m 5 ) − 2 adalah ....

Hasil pemangkatan dari $(4 m^{5})^{- 2}$ adalah $....$

$fraction numerator 1 over denominator m fourth root of m cubed end root end fraction$
$fraction numerator 1 over denominator m squared space fourth root of m squared end root end fraction$

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R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat: jika bilangan positif maka berlaku Sehingga diperoleh sebagai berikut. Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat yaitu maka Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat pecahan sehingga Jadi h asil pemangkatan dari adalah . Oleh karena itu, jawaban yang benar adalah D.

Ingat: jika a not equal to 0 space text dan end text space m comma space n bilangan positif maka berlaku

n-th root of a to the power of m end root equals a to the power of m over n end exponent

Sehingga open parentheses fourth root of m to the power of 5 end root close parentheses to the power of negative 2 end exponent diperoleh sebagai berikut.

open parentheses fourth root of m to the power of 5 end root close parentheses to the power of negative 2 end exponent equals open parentheses m to the power of 5 over 4 end exponent close parentheses to the power of negative 2 end exponent

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fourth root of m to the power of 5 end root close parentheses to the power of negative 2 end exponent end cell equals cell open parentheses m to the power of 5 over 4 end exponent close parentheses to the power of negative 2 end exponent end cell row blank equals cell m to the power of 5 over 4 cross times open parentheses negative 2 close parentheses end exponent end cell row blank equals cell m to the power of fraction numerator negative 10 over denominator 4 end fraction end exponent end cell row blank equals cell m to the power of negative 10 over 4 end exponent end cell end table$

Berdasarkan sifat bilangan berpangkat yaitu a to the power of negative n end exponent equals 1 over a to the power of n comma space a not equal to 0 maka

Berdasarkan sifat bilangan berpangkat a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fourth root of m to the power of 5 end root close parentheses to the power of negative 2 end exponent end cell equals cell 1 over m to the power of begin display style 10 over 4 end style end exponent end cell row blank equals cell 1 over m to the power of begin display style fraction numerator 8 plus 2 over denominator 4 end fraction end style end exponent end cell row blank equals cell 1 over m to the power of begin display style 8 over 4 end style plus begin display style 2 over 4 end style end exponent end cell row blank equals cell 1 over m to the power of 2 plus begin display style 2 over 4 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator m squared cross times m to the power of begin display style 2 over 4 end style end exponent end fraction end cell end table$

Berdasarkan sifat bilangan berpangkat pecahan a to the power of m over n end exponent equals n-th root of a to the power of m end root comma space a not equal to 0 sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fourth root of m to the power of 5 end root close parentheses to the power of negative 2 end exponent end cell equals cell fraction numerator 1 over denominator m squared cross times m to the power of begin display style 2 over 4 end style end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator m squared cross times fourth root of m squared end root end fraction end cell row blank equals cell fraction numerator 1 over denominator m squared space fourth root of m squared end root end fraction end cell end table$

Jadi hasil pemangkatan dari open parentheses fourth root of m to the power of 5 end root close parentheses to the power of negative 2 end exponent adalah $fraction numerator 1 over denominator m squared space fourth root of m squared end root end fraction$ .

Oleh karena itu, jawaban yang benar adalah D.